Numerical solution of linear integral equations system using the Bernstein collocation method

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 2 Absolute errors for Example 1

$t = \frac{1}{2^{r}}$	Presented method		ANN method		TQR
$t = \frac{1}{2^{r}}$	$e_{1, 4} (t)$	$e_{2, 4} (t)$	$e_{1, 4} (t)$	$e_{2, 4} (t)$	$e_{1, 4} (t)$	$e_{2, 4} (t)$
r = 1	3.50 × 10⁻⁶	1.17 × 10⁻⁵	7.32 × 10⁻⁴	3.84 × 10⁻⁴	4.11 × 10⁻⁴	7.35 × 10⁻⁴
r = 2	2.90 × 10⁻⁶	1.06 × 10⁻⁵	1.15 × 10⁻⁴	5.62 × 10⁻⁴	3.81 × 10⁻⁴	5.14 × 10⁻⁴
r = 3	4.78 × 10⁻⁵	2.50 × 10⁻⁴	5.34 × 10⁻⁴	6.11 × 10⁻⁴	1.29 × 10⁻²	8.41 × 10⁻⁴
r = 4	5.03 × 10⁻⁵	2.50 × 10⁻⁴	6.71 × 10⁻⁴	6.30 × 10⁻⁴	4.17 × 10⁻³	3.28 × 10⁻³
r = 5	3.71 × 10⁻⁵	1.63 × 10⁻⁴	9.80 × 10⁻⁴	3.27 × 10⁻⁴	2.08 × 10⁻³	8.20 × 10⁻⁴
r = 6	2.53 × 10⁻⁵	8.90 × 10⁻⁵	1.17 × 10⁻⁴	4.83 × 10⁻⁴	3.27 × 10⁻³	3.53 × 10⁻³
r = 7	1.79 × 10⁻⁵	4.30 × 10⁻⁵	4.15 × 10⁻⁴	4.88 × 10⁻⁴	1.08 × 10⁻²	2.71 × 10⁻²
r = 8	1.37 × 10⁻⁵	1.77 × 10⁻⁵	3.12 × 10⁻⁴	4.87 × 10⁻⁴	6.31 × 10⁻³	3.84 × 10⁻⁴
r = 9	1.16 × 10⁻⁵	4.30 × 10⁻⁶	1.16 × 10⁻⁴	4.82 × 10⁻⁴	2.10 × 10⁻⁴	3.84 × 10⁻³